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You might consider it an arbitrary definition. However, it is one that makes sense. Look at this sequence:

10 to the power 3 = 1000

10 to the power 2 = 100

10 to the power 1 = 10

10 to the power 0 = ???

10 to the power -1 = ???

10 to thepower -2 = ???

What number would you logically place there? Look at the two sequences - the exponents get reduce by 1 at a time, and the result gets reduced by a factor of 10 every time. If you logically continue this, you get the result that 10 to the power 0 is 1, and you also get reasonable expressions for negative powers.

More formally, certain rules of exponents will continue being valid when powers are defined this way; in this case, mainly, (x to the power a) times (x to the power b) = x to the power (a + b). This continues to be valid ONLY if x to the power zero is defined as 1.

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Q: Why is a nonzero number raised to the zero power equals one?
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